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Actually, I want to know whether there are explicit and formal definitions of the properties which are authenticity, integrality or non-repudiation.

It seems that the signatures and MACs can achieve the authenticity, integrality, non-repudiation and unforgeability. However, there is only a unforgeable experiment when we consider the security of signatures or MACs.

Q1: What about other three types of security experiments? Are there the formal definitions of the security experiments of the other three properties?

Q2: What are the relations among these four properties? (Anyway, how to prove the relation formally, if there are not a formal definitions?)

If the unforgeability implies the others which means that ungorgebility is the strongest notion among these four properties, then I think I can regard this conclusion as the answer of Q1. If any pair of these four properties are separation, there must exist a scheme which only achieves any part of these four properties. (I know that a scheme which cannot achieve all these four properties is not secure. I just want to consider the existence of them in order to know the relation among these four properties.)

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  • $\begingroup$ Are you interested in the relation ship between the security properties the algorithms achieve, or the functioning of the algorithms from the inside? I suggest restructure the question to make the separation clear. $\endgroup$ – DannyNiu Apr 9 '20 at 2:24
  • $\begingroup$ @DannyNiu The first one I think, let me modify it. $\endgroup$ – TeamBright Apr 10 '20 at 3:14
  • $\begingroup$ Typos: integrality should be integrity; ungorgebility should be unforgeability. $\endgroup$ – fgrieu Sep 7 '20 at 17:02
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The 3 properties have commonly accepted meaning in Cryptography:

  • Authenticity: The message comes from the party associated with the verification key.

  • Integrity: The message had not been modified.

  • Non-repudiation: The signer cannot deny themselves signing the message.

We usually model the security against the weakest point of the signature/MAC - being forged; whereas other types of attacks such as key-recovery automatically implies the algorithm is insecure.

The unforgeability implies the other 3 (2 in case of MAC) properties, because the ability to forge a signature/MAC under a particular algorithm implies that

  1. the message may come from someone capable of forging the signagure/MAC (authenticity),

  2. capable of modifying a signed message (integrity), and

  3. capable of signing messages against the wish of the holder of the private key (non-repudiation).

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  • $\begingroup$ Do you mean that the unforgeability is the weakest one? As you say, if a signature/MAC is not unforgeability (someone has the ability to forge it), then it cannot achieve any one of other 3 properties. In other words, if it achieves any one of these 3 properiies, the it also achieves unforgeability. $\endgroup$ – TeamBright Apr 10 '20 at 5:35
  • $\begingroup$ I mean forgery is often the cheapest aspect of a signature/MAC to attack. A signature/MAC has to achieve all of the 3/2 properties to be unforgeable. $\endgroup$ – DannyNiu Apr 10 '20 at 10:48
  • $\begingroup$ But the security game only captures the unforgeability, which means that a unforgeabe signature/MAC may not achieve other properties. How can we prove or guarantee that a unforgeabe signature/MAC also achieves other 3/2 properties. $\endgroup$ – TeamBright Apr 10 '20 at 12:50
  • $\begingroup$ @TeamBright "How can we prove or guarantee" - through simple reasoning of course. If you firmly question such reasoning, I'll be glad if you can demonstrate its flaw, empirically, logically, or by citing a reference. $\endgroup$ – DannyNiu Apr 13 '20 at 1:39
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One thing I'd like to point out clearly is that MAC is not a digital signature. MACs offer authenticity and integrality, but not non-repudiation. MACs are generated using shared secret (symmetric key). Non-repudation can be discussed only in the context of public key cryptography.

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